States, goals and values: Revisiting practical reasoning

4.1.Relation to other work

Now that we have spelled out the details of our approach, before we demonstrate it through application to different scenarios we compare and relate the approach to other work on practical reasoning in multi-agent systems. Argumentation has been used as a basis for a number of different proposals for how to handle practical reasoning and decision-making in agent systems, for example, [2,15,18,26,32]. For our discussion here we compare our work with a general model for agent reasoning (the BDI model), given in textbooks such as [34] and another approach [26] that is specifically grounded in argumentation.

5.1.Trains and tunnels

We begin with the example used to illustrate the original AATS as introduced in [35]. There are two trains, one of which (E) is Eastbound, the other of which (W) is Westbound, each occupying their own circular track. At one point, both tracks pass through a narrow tunnel and a crash will occur if both trains are in the tunnel at the same time. Each train is an agent (i.e. Ag={E,W}), and both have their position described by reference to the tunnel: a train can be away (has just left the tunnel), waiting (about to enter the tunnel) or in (the tunnel). Φ thus contains six propositions: {awayE,waitingE,inE,awayW,waitingW,inW}. Initially both trains are away. Both agents have two actions, movei or idlei. Idlei means that the position of i does not change. Movei takes i from away to waiting, from waiting to in and from in to waiting. This gives the AATS shown in Fig. 1 along with a key to explain the labels. A train may move or idle in any state, except where both are in: after a crash no further movement is possible.

Fig. 1.

AATS for Trains scenario. AW = east away, west waiting, etc. i,m= east idle, west moves, etc. Moves where both are idle will return to the same state and are not shown here.

We define one term in Θ. We say that crash←inE∧inW.

The agents will have two values: Progress and Safety, the first promoted by moving, the second demoted by a crash. Thus the basic Δ is the same for both agents in this case:

Each agent can now form its own Δi by introducing the appropriate subscripts.

Now we can see that Progress will motivate movement to the next state through an achievement goal, while Safety will motivate idling as an avoidance goal in the state where both trains are waiting. This gives rise to the arguments:33

If we now assume that trains prefer Safety to Progress, they will both prefer Arg2 and so they will get stuck in waiting, since Arg1 will be open to an objection based on CQ9:

Suppose, however, we add a clause to Θ

Now we revise the value theory for E; instead of seeing Progress as promoted by any movement, E now believes it to be promoted only by moving when it is sure that it is safe to do so. This means that ΔE becomes:

Now this additional knowledge that Progress will not be promoted by entering the tunnel unless it is safe to do so will mean that the agent E will only have an argument to enter the tunnel when it is safe to do so. Thus E will replace Arg1 with Arg1E.

This argument is not subject to Obj1. It will not, however, ensure deadlock is avoided. Obj1 still applies to W and a preference for Safety will mean that W will continue to wait, and so E may never know that it is safe to enter, and so will be unable to deploy Arg1E. E will thus not have an argument to move when it is waiting. So let us look at CQ9 a little further.

For the objection such as Obj1, arising from CQ9, to be effective, three things are needed. As noted, Safety has to be preferred to Progress. Thus deadlock could be avoided if W was sufficiently impatient that it came to disregard safety, and prefer progress, so that Arg1 defeats Arg2. Second, the agent must believe that the state is such that both are waiting. If W can see that E is away, then it can move with confidence, since it nows that Arg2 is not effective since it cannot in practice demote safety. Otherwise, however, it is a risk to assume that this is not the state. Finally a crash will only occur if E chooses to move rather than idle. So W can move and hope that E will choose to be idle. This is open to a further objection based on CQ17,

If, however, W knows that E is using ΔE, then it can rebut CQ17 by stating that E has no argument to move to in while W is not away. Thus deadlock can be avoided given this awareness of the arguments available to the other agents involved. Of course, deadlock can also be avoided by improving information through a signalling system, or through a social convention as in [35]. Note also that whereas the goals of the agents are implicit or assumed in [35], here they are derived from the explicit and individual values represented in the programs ΔW and ΔE.

To summarise: this example illustrates:

5.2.Should I stay or should I go?

For our second example we look at the choice between career and domestic life. We assume two agents, Mary and Jane, who have the option taking a new job, which will give them a better job, making them famous and paying more money, but which will mean that they have to live away from their partner; or refusing the offer which will allow them to continue to live with their partner, but lose the career opportunity.

For the example we will consider only what is necessary for the example: some larger system may be assumed. In this example there is no interaction between the agents, and so we can consider them separately. Accordingly the AATS will be applicable to both Mary and Jane (both agents thinking of themselves as “me”, hence suffix “m”, and their partner as “p”). The action options are move or stay. From the initial state move will reach a state in which richm and famousm become true, and locationUKm becomes false and locationAustraliam becomes true. For both Mary and Jane hasPartnerm is true. The partner’s location remains unchanged, so that locationUKp stays true and locationAustraliap remains false.

We now introduce some defined terms in Θ. First we define successfulm as richm and famousm, and separatedm as (locationUKm and locationUKp) or (locationAustraliam and locationAustraliap).

The relevant AATS fragment is shown in Fig. 2.

Fig. 2.

AATS for Mary and Jane scenario.

Now we define Δ. Both Mary and Jane have the values of Money, promoted by being rich, Relationship, promoted by hasPartnerm and Happiness, which is defined differently for the two agents. Jane craves success and so ΔJane contains the clause

Note that here the current value of successful does not matter: if it is currently true it is a maintenance goal and if false it is an achievement goal. Mary, on the other hand, is more interested in her relationship than success, so that ΔMary is:

If hasPartner holds, separated is an avoidance goal if it is currently false and a remedy goal if it is currently true. If hasPartner is currently false, finding a partner in the right country becomes an achievement goal.

Now consider the choice that Mary and Jane must make. We can now see that Money will be promoted for both by move. The value Relationships will be neither promoted nor demoted since hasPartnerm remains true. But for Jane, Happiness is promoted because successfulm is achieved, whereas for Mary, Happiness is demoted since separatedm becomes true, and success is not a relevant consideration for her. Thus Jane will choose to move and Mary will, if Happiness is preferred to Money, choose to stay. Note that it may well be that both Mary and Jane rank Relationships above Money, and may even rank Relationships above Happiness: the point is that Jane expects to be able to cope with a long distance relationship and Mary does not.

Now suppose that Mary wanted to challenge Jane’s decision. Although both are entirely agreed on the problem formulation, share the same values, and have used the AATS correctly in accordance with their own preferences, they disagree on whether Happiness will be promoted or demoted (CQ4 from [4]) and so label the move transition differently. Now, however, we can debate which labelling is correct since their Δs contain a justification for their different labellings. Mary can suggest her own Happiness rules to Jane – will you really be happy in a long distance relationship? Alternatively Jane may urge her own views on Happiness to Mary – will you not be made unhappy by giving up the prospect of success? Note, however, that even if they do succeed in convincing one another that both success and separation are relevant to happiness, they may still make different decisions. If we consider the program ΔJane∪ΔMary, we can see that we can satisfy clauses both for the promotion and demotion of Happiness, and so the priority between the clauses becomes significant. This example therefore shows that preferences as to how values are promoted, as well as preferences between values, may affect the decision. In effect this is implementing CQ8, but using the priorities incorporated in Δi to avoid marking the transitions with conflicting labels and complicating the evaluation of arguments derived from the AATS.

So far we have, like previous work such as [4], used an ordering on values to adjudicate conflicts between arguments. Our new machinery for considering goals, however, offers an opportunity for a different basis for choice. If we just consider the program ΔJane∪ΔMary, and the value of Happiness, we can see that an agent using this program will have both avoidance and achievement goals relating to this value. Now there is some evidence to suggest that people tend to have a to have strong preference for avoiding losses over acquiring gains. This phenomenon, known as loss aversion, was described in [17], and can be used to explain differences in the way in which a problem is framed affects how subjects respond in behavioural economics experiments (e.g. [7]). If we accept this theory we should always prefer avoidance and maintenance goals to achievement and remedy goals, and in this case choose to stay rather than go. This could be used as a general principle for prioritising the clauses for a value in Δ. If, however, we wished to give even greater importance to loss aversion, we could first order actions on the basis of the nature of the goal, and then use value preferences to break ties. In the example, even if a loss-adverse Mary were to prefer Money to Happiness, she would still choose to stay, since the loss of Happiness would outweigh the gain in Money. Only if she was faced with threats to both values would their ordering come into consideration. We leave consideration of detailed arguments about value preferences for future work; mechanisms for reasoning about preferences were provided in [21] and relating our approach to ASPIC+ [23] will enable this strand of reasoning to be explored further.

We have used this example to illustrate in particular:

Our third example will illustrate the distinction used in [10] between values which have no effect after they have reached a certain threshold (satisficers) and those which are always considered beneficial (maximisers). Whilst there are other approaches in the argumentation literature that capture reasoning about preferences between goals (e.g. [15]), we show through the example how reasoning about preferences may play a secondary role to the need to attain satisfactory levels for the various motivating values involved in the scenario.

5.3.Enough is enough

This example concerns an agent trying to strike an appropriate balance between work and leisure. Employees often have some say over how many hours they will work, and may choose the extra leisure or the extra money according to their individual preferences. We model this situation in the AATS fragment of Fig. 3. The propositions of interest are hoursWorked, freeTime and hourlyRate.

Fig. 3.

AATS for Working Hours scenario.

In Θ we define income as the product of hoursWorked and hourlyRate. Agents can increase their hours, which increases hoursWorked (and hence income), but decreases freeTime. Of course, whether the agent is free to choose its hours depends on the employer. The more traditional situation is for overtime to be offered, but not a reduction in standard hours (although currently so-called flexible working is becoming increasingly available). For this reason when we consider the joint actions with the employer the option to work less may not always be available.

Often economics assumes that when people make decisions they always prefer more of a good. Empirical work, however, suggests they can been seen as maximisers or satificers (e.g. [30]), and can also adopt different attitudes towards different values. While maximisers always seek to maximise their criteria, satificers set a threshold for particular criteria, and once the threshold is reached that criterion ceases to have any effect. In practice, as the notion of diminishing marginal returns suggests, for most goods the additional utility of a given amount decreases as more of that good is acquired; satisficing can be seen as an extreme application of this principle: at a certain point more adds no additional utility at all. When combined with the notion of loss aversion [17] discussed in the previous example, we can see that choice may be a good deal more complicated than a simple application of preferences.

Now consider possible rules for Δ. We have two values, Money and Leisure. Because income and freeTime are continuous variables rather than Booleans, the third term in the body clauses will here be an integer rather than one of {T,F}. Possible rules for maximisers are:

But for satisficers, the rules will be:

Agents may mix and match these rules: they may be maximisers for both values (M1–M4), satisficers for both values (S1–S4), money maximisers and leisure satisficers (M1, M2, S3 and S4), or money satisficers and leisure maximisers (S1, S2, M3 and M4). We will term the agents MMLM (i.e. money maximiser and leisure maximiser), MSLS, MMLS and MSLM respectively. Loss aversion can be effected by giving the demotion rules priority over the promotion rules. Where they are maximisers of one value and satificers of another they may tend to prefer satisficing to maximising. Thus a money satisficer and leisure maximiser will order the rules M4, M3, S2 and S1. Alternatively the agent may express its preferences in terms of values rather than the general principles. We will represent this value preference by the order of the values and qualifiers: thus in the case of the double maximiser, MMLM prefers money to leisure and LMMM prefers leisure to money.

Now consider that AATS fragment in Fig. 3, where the hourly rate is fixed at 10. Agents may choose to increase their hours, or stay the same (we assume that the employer is not making the reduced hours option available: the symmetry means that we can make this simplification without loss of generality). Suppose working eight hours is the initial state. Let us now consider our various agents in turn. We will assume that agents are not loss adverse in general, but will not wish to fall below a satisfied threshold for one value for the sake of improving the other, even where that other value is preferred.

The satisficers will have different choices according to their thresholds. There are four situations: both thresholds are satisfied, MT is satisfied while LT is not, LT is satisfied while MT is not, and neither is satisfied. These four possibilities are applicable to both the current and the next state. The first eight rows of Table 1 summarise the choices made by the various agents in the various situations.

The double maximiser will have an achievement goal based on money to increase its hours, but an avoidance goal based on leisure to refuse the extra hours. Since thresholds are not applicable to these agents, the choice will be based on value preferences: MMLM will increase its hours and LMMM will keep them the same.

The double satisficer will only have arguments to increase its hours when the money threshold is not already satisfied, and will only have arguments against increasing its hours where the leisure threshold will cease to be satisfied as a result. Only where neither threshold is satisfied in both states will the preference between the values determine the action.

The money maximiser and leisure satisficer will always have a reason to increase its hours but will only have a reason not to increase its hours if this would take it below its leisure threshold. Here the value preference makes a difference only if the leisure threshold is unsatisfied in neither state. Similarly the value preference makes a difference to the money satisficer and leisure maximiser only where the money threshold is satisfied in neither state.

What this shows is that we can get a variety of behaviour, even when agents share value orderings. Whereas maximisers will always act in accordance with the pure value preference, the influence of this preference decreases when the agents are satisficing values.

This also has implications for an employer who wishes to encourage staff to work overtime. The obvious course would be to increase wages. But suppose we assume that all staff currently satisfy their thresholds. Now an increase in hourly rate will only attract money maximisers, and, where the additional hours would take the agent below their leisure threshold, not even these. Note that in this case, where both thresholds are satisfied initially, the value preferences of the workers do not make a difference at all: money maximisers will accept the extra hours only if it does not jeopardise their leisure threshold, and money satisfiers will not be interested. Worse for the employer is that the increase in wages may enable leisure maximisers to reduce their hours while keeping above their money threshold, and so the increased wage will result in fewer hours worked by such agents. It is probably for this reason that overtime hours are often offered at a premium rate, not applicable to the basic hours. But the effect may still cause problems with staff with no standard hours, for example, casual bar staff.

Perversely, the employers may be able to attract more employees to overtime by cutting pay, since this may bring the money satisficers below their thresholds, as illustrated by the last two rows of Table 1. Here the wage cut may cause the money threshold to cease to be satisfied: the leisure threshold can be satisfied by keeping the same hours, and may or may not cease to be satisfied if hours are increased. Now all agents (except the double maximisers with a preference for leisure) will accept the overtime provided that they will remain above the leisure threshold, so as to restore, or approach their money threshold. All agents who value money more than leisure will accept the overtime, even if this takes them below the leisure threshold (effectively, if neither threshold can be satisfied, all agents become double maximisers). This phenomenon is similar to that of the Giffen Good in economics (see, e.g., [19]), where raising the price of a good increases demand (whereas the normal expectation is the demand falls when price rises). The classic example given by Marshall [19] is of less desirable foods, whose demand is driven by poverty. People will satisfy their hunger with a combination of basics, such as bread, and luxury foods, such as ham. If the price of bread rises, they must buy less ham to afford sufficient bread to maintain the calorie level, and bread consumption will need to rise to replace the ham they can no longer afford. Such people are, in our terms, bread satisficers and ham maximisers.

To summarise this example, it illustrates: